metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.155D14, C14.972- (1+4), C4⋊C4.211D14, C28⋊2Q8⋊33C2, C42.C2⋊11D7, (C2×C28).92C23, C4.Dic14⋊37C2, C42⋊D7.7C2, Dic7⋊3Q8⋊38C2, C28.131(C4○D4), (C2×C14).241C24, (C4×C28).200C22, D14⋊2Q8.12C2, C4.20(Q8⋊2D7), D14⋊C4.112C22, C4⋊Dic7.244C22, C22.262(C23×D7), Dic7⋊C4.124C22, C7⋊5(C22.35C24), (C4×Dic7).146C22, (C2×Dic7).261C23, (C22×D7).106C23, C2.60(D4.10D14), (C2×Dic14).182C22, C4⋊C4⋊D7.3C2, C14.118(C2×C4○D4), C2.25(C2×Q8⋊2D7), (C7×C42.C2)⋊14C2, (C2×C4×D7).131C22, (C7×C4⋊C4).196C22, (C2×C4).206(C22×D7), SmallGroup(448,1150)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 764 in 192 conjugacy classes, 95 normal (19 characteristic)
C1, C2, C2 [×2], C2, C4 [×2], C4 [×13], C22, C22 [×3], C7, C2×C4, C2×C4 [×6], C2×C4 [×9], Q8 [×4], C23, D7, C14, C14 [×2], C42, C42 [×5], C22⋊C4 [×6], C4⋊C4 [×6], C4⋊C4 [×14], C22×C4, C2×Q8 [×2], Dic7 [×7], C28 [×2], C28 [×6], D14 [×3], C2×C14, C42⋊C2, C4×Q8 [×2], C22⋊Q8 [×2], C42.C2, C42.C2 [×4], C42⋊2C2 [×4], C4⋊Q8, Dic14 [×4], C4×D7 [×2], C2×Dic7, C2×Dic7 [×6], C2×C28, C2×C28 [×6], C22×D7, C22.35C24, C4×Dic7, C4×Dic7 [×4], Dic7⋊C4 [×6], C4⋊Dic7 [×8], D14⋊C4 [×6], C4×C28, C7×C4⋊C4 [×6], C2×Dic14 [×2], C2×C4×D7, C28⋊2Q8, C42⋊D7, Dic7⋊3Q8 [×2], C4.Dic14 [×4], D14⋊2Q8 [×2], C4⋊C4⋊D7 [×4], C7×C42.C2, C42.155D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×2], C24, D14 [×7], C2×C4○D4, 2- (1+4) [×2], C22×D7 [×7], C22.35C24, Q8⋊2D7 [×2], C23×D7, C2×Q8⋊2D7, D4.10D14 [×2], C42.155D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=b2, d2=a2, ab=ba, cac-1=dad-1=a-1, cbc-1=a2b-1, dbd-1=b-1, dcd-1=a2b2c13 >
►On 224 points
Generators in S224
(1 151 48 137)(2 138 49 152)(3 153 50 139)(4 140 51 154)(5 155 52 113)(6 114 53 156)(7 157 54 115)(8 116 55 158)(9 159 56 117)(10 118 29 160)(11 161 30 119)(12 120 31 162)(13 163 32 121)(14 122 33 164)(15 165 34 123)(16 124 35 166)(17 167 36 125)(18 126 37 168)(19 141 38 127)(20 128 39 142)(21 143 40 129)(22 130 41 144)(23 145 42 131)(24 132 43 146)(25 147 44 133)(26 134 45 148)(27 149 46 135)(28 136 47 150)(57 172 203 92)(58 93 204 173)(59 174 205 94)(60 95 206 175)(61 176 207 96)(62 97 208 177)(63 178 209 98)(64 99 210 179)(65 180 211 100)(66 101 212 181)(67 182 213 102)(68 103 214 183)(69 184 215 104)(70 105 216 185)(71 186 217 106)(72 107 218 187)(73 188 219 108)(74 109 220 189)(75 190 221 110)(76 111 222 191)(77 192 223 112)(78 85 224 193)(79 194 197 86)(80 87 198 195)(81 196 199 88)(82 89 200 169)(83 170 201 90)(84 91 202 171)
(1 202 15 216)(2 71 16 57)(3 204 17 218)(4 73 18 59)(5 206 19 220)(6 75 20 61)(7 208 21 222)(8 77 22 63)(9 210 23 224)(10 79 24 65)(11 212 25 198)(12 81 26 67)(13 214 27 200)(14 83 28 69)(29 197 43 211)(30 66 44 80)(31 199 45 213)(32 68 46 82)(33 201 47 215)(34 70 48 84)(35 203 49 217)(36 72 50 58)(37 205 51 219)(38 74 52 60)(39 207 53 221)(40 76 54 62)(41 209 55 223)(42 78 56 64)(85 117 99 131)(86 146 100 160)(87 119 101 133)(88 148 102 162)(89 121 103 135)(90 150 104 164)(91 123 105 137)(92 152 106 166)(93 125 107 139)(94 154 108 168)(95 127 109 113)(96 156 110 142)(97 129 111 115)(98 158 112 144)(114 190 128 176)(116 192 130 178)(118 194 132 180)(120 196 134 182)(122 170 136 184)(124 172 138 186)(126 174 140 188)(141 189 155 175)(143 191 157 177)(145 193 159 179)(147 195 161 181)(149 169 163 183)(151 171 165 185)(153 173 167 187)
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28)(29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56)(57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84)(85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112)(113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140)(141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168)(169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196)(197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224)
(1 14 48 33)(2 32 49 13)(3 12 50 31)(4 30 51 11)(5 10 52 29)(6 56 53 9)(7 8 54 55)(15 28 34 47)(16 46 35 27)(17 26 36 45)(18 44 37 25)(19 24 38 43)(20 42 39 23)(21 22 40 41)(57 68 203 214)(58 213 204 67)(59 66 205 212)(60 211 206 65)(61 64 207 210)(62 209 208 63)(69 84 215 202)(70 201 216 83)(71 82 217 200)(72 199 218 81)(73 80 219 198)(74 197 220 79)(75 78 221 224)(76 223 222 77)(85 190 193 110)(86 109 194 189)(87 188 195 108)(88 107 196 187)(89 186 169 106)(90 105 170 185)(91 184 171 104)(92 103 172 183)(93 182 173 102)(94 101 174 181)(95 180 175 100)(96 99 176 179)(97 178 177 98)(111 192 191 112)(113 118 155 160)(114 159 156 117)(115 116 157 158)(119 140 161 154)(120 153 162 139)(121 138 163 152)(122 151 164 137)(123 136 165 150)(124 149 166 135)(125 134 167 148)(126 147 168 133)(127 132 141 146)(128 145 142 131)(129 130 143 144)
G:=sub<Sym(224)| (1,151,48,137)(2,138,49,152)(3,153,50,139)(4,140,51,154)(5,155,52,113)(6,114,53,156)(7,157,54,115)(8,116,55,158)(9,159,56,117)(10,118,29,160)(11,161,30,119)(12,120,31,162)(13,163,32,121)(14,122,33,164)(15,165,34,123)(16,124,35,166)(17,167,36,125)(18,126,37,168)(19,141,38,127)(20,128,39,142)(21,143,40,129)(22,130,41,144)(23,145,42,131)(24,132,43,146)(25,147,44,133)(26,134,45,148)(27,149,46,135)(28,136,47,150)(57,172,203,92)(58,93,204,173)(59,174,205,94)(60,95,206,175)(61,176,207,96)(62,97,208,177)(63,178,209,98)(64,99,210,179)(65,180,211,100)(66,101,212,181)(67,182,213,102)(68,103,214,183)(69,184,215,104)(70,105,216,185)(71,186,217,106)(72,107,218,187)(73,188,219,108)(74,109,220,189)(75,190,221,110)(76,111,222,191)(77,192,223,112)(78,85,224,193)(79,194,197,86)(80,87,198,195)(81,196,199,88)(82,89,200,169)(83,170,201,90)(84,91,202,171), (1,202,15,216)(2,71,16,57)(3,204,17,218)(4,73,18,59)(5,206,19,220)(6,75,20,61)(7,208,21,222)(8,77,22,63)(9,210,23,224)(10,79,24,65)(11,212,25,198)(12,81,26,67)(13,214,27,200)(14,83,28,69)(29,197,43,211)(30,66,44,80)(31,199,45,213)(32,68,46,82)(33,201,47,215)(34,70,48,84)(35,203,49,217)(36,72,50,58)(37,205,51,219)(38,74,52,60)(39,207,53,221)(40,76,54,62)(41,209,55,223)(42,78,56,64)(85,117,99,131)(86,146,100,160)(87,119,101,133)(88,148,102,162)(89,121,103,135)(90,150,104,164)(91,123,105,137)(92,152,106,166)(93,125,107,139)(94,154,108,168)(95,127,109,113)(96,156,110,142)(97,129,111,115)(98,158,112,144)(114,190,128,176)(116,192,130,178)(118,194,132,180)(120,196,134,182)(122,170,136,184)(124,172,138,186)(126,174,140,188)(141,189,155,175)(143,191,157,177)(145,193,159,179)(147,195,161,181)(149,169,163,183)(151,171,165,185)(153,173,167,187), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84)(85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196)(197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224), (1,14,48,33)(2,32,49,13)(3,12,50,31)(4,30,51,11)(5,10,52,29)(6,56,53,9)(7,8,54,55)(15,28,34,47)(16,46,35,27)(17,26,36,45)(18,44,37,25)(19,24,38,43)(20,42,39,23)(21,22,40,41)(57,68,203,214)(58,213,204,67)(59,66,205,212)(60,211,206,65)(61,64,207,210)(62,209,208,63)(69,84,215,202)(70,201,216,83)(71,82,217,200)(72,199,218,81)(73,80,219,198)(74,197,220,79)(75,78,221,224)(76,223,222,77)(85,190,193,110)(86,109,194,189)(87,188,195,108)(88,107,196,187)(89,186,169,106)(90,105,170,185)(91,184,171,104)(92,103,172,183)(93,182,173,102)(94,101,174,181)(95,180,175,100)(96,99,176,179)(97,178,177,98)(111,192,191,112)(113,118,155,160)(114,159,156,117)(115,116,157,158)(119,140,161,154)(120,153,162,139)(121,138,163,152)(122,151,164,137)(123,136,165,150)(124,149,166,135)(125,134,167,148)(126,147,168,133)(127,132,141,146)(128,145,142,131)(129,130,143,144)>;
G:=Group( (1,151,48,137)(2,138,49,152)(3,153,50,139)(4,140,51,154)(5,155,52,113)(6,114,53,156)(7,157,54,115)(8,116,55,158)(9,159,56,117)(10,118,29,160)(11,161,30,119)(12,120,31,162)(13,163,32,121)(14,122,33,164)(15,165,34,123)(16,124,35,166)(17,167,36,125)(18,126,37,168)(19,141,38,127)(20,128,39,142)(21,143,40,129)(22,130,41,144)(23,145,42,131)(24,132,43,146)(25,147,44,133)(26,134,45,148)(27,149,46,135)(28,136,47,150)(57,172,203,92)(58,93,204,173)(59,174,205,94)(60,95,206,175)(61,176,207,96)(62,97,208,177)(63,178,209,98)(64,99,210,179)(65,180,211,100)(66,101,212,181)(67,182,213,102)(68,103,214,183)(69,184,215,104)(70,105,216,185)(71,186,217,106)(72,107,218,187)(73,188,219,108)(74,109,220,189)(75,190,221,110)(76,111,222,191)(77,192,223,112)(78,85,224,193)(79,194,197,86)(80,87,198,195)(81,196,199,88)(82,89,200,169)(83,170,201,90)(84,91,202,171), (1,202,15,216)(2,71,16,57)(3,204,17,218)(4,73,18,59)(5,206,19,220)(6,75,20,61)(7,208,21,222)(8,77,22,63)(9,210,23,224)(10,79,24,65)(11,212,25,198)(12,81,26,67)(13,214,27,200)(14,83,28,69)(29,197,43,211)(30,66,44,80)(31,199,45,213)(32,68,46,82)(33,201,47,215)(34,70,48,84)(35,203,49,217)(36,72,50,58)(37,205,51,219)(38,74,52,60)(39,207,53,221)(40,76,54,62)(41,209,55,223)(42,78,56,64)(85,117,99,131)(86,146,100,160)(87,119,101,133)(88,148,102,162)(89,121,103,135)(90,150,104,164)(91,123,105,137)(92,152,106,166)(93,125,107,139)(94,154,108,168)(95,127,109,113)(96,156,110,142)(97,129,111,115)(98,158,112,144)(114,190,128,176)(116,192,130,178)(118,194,132,180)(120,196,134,182)(122,170,136,184)(124,172,138,186)(126,174,140,188)(141,189,155,175)(143,191,157,177)(145,193,159,179)(147,195,161,181)(149,169,163,183)(151,171,165,185)(153,173,167,187), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84)(85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196)(197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224), (1,14,48,33)(2,32,49,13)(3,12,50,31)(4,30,51,11)(5,10,52,29)(6,56,53,9)(7,8,54,55)(15,28,34,47)(16,46,35,27)(17,26,36,45)(18,44,37,25)(19,24,38,43)(20,42,39,23)(21,22,40,41)(57,68,203,214)(58,213,204,67)(59,66,205,212)(60,211,206,65)(61,64,207,210)(62,209,208,63)(69,84,215,202)(70,201,216,83)(71,82,217,200)(72,199,218,81)(73,80,219,198)(74,197,220,79)(75,78,221,224)(76,223,222,77)(85,190,193,110)(86,109,194,189)(87,188,195,108)(88,107,196,187)(89,186,169,106)(90,105,170,185)(91,184,171,104)(92,103,172,183)(93,182,173,102)(94,101,174,181)(95,180,175,100)(96,99,176,179)(97,178,177,98)(111,192,191,112)(113,118,155,160)(114,159,156,117)(115,116,157,158)(119,140,161,154)(120,153,162,139)(121,138,163,152)(122,151,164,137)(123,136,165,150)(124,149,166,135)(125,134,167,148)(126,147,168,133)(127,132,141,146)(128,145,142,131)(129,130,143,144) );
G=PermutationGroup([(1,151,48,137),(2,138,49,152),(3,153,50,139),(4,140,51,154),(5,155,52,113),(6,114,53,156),(7,157,54,115),(8,116,55,158),(9,159,56,117),(10,118,29,160),(11,161,30,119),(12,120,31,162),(13,163,32,121),(14,122,33,164),(15,165,34,123),(16,124,35,166),(17,167,36,125),(18,126,37,168),(19,141,38,127),(20,128,39,142),(21,143,40,129),(22,130,41,144),(23,145,42,131),(24,132,43,146),(25,147,44,133),(26,134,45,148),(27,149,46,135),(28,136,47,150),(57,172,203,92),(58,93,204,173),(59,174,205,94),(60,95,206,175),(61,176,207,96),(62,97,208,177),(63,178,209,98),(64,99,210,179),(65,180,211,100),(66,101,212,181),(67,182,213,102),(68,103,214,183),(69,184,215,104),(70,105,216,185),(71,186,217,106),(72,107,218,187),(73,188,219,108),(74,109,220,189),(75,190,221,110),(76,111,222,191),(77,192,223,112),(78,85,224,193),(79,194,197,86),(80,87,198,195),(81,196,199,88),(82,89,200,169),(83,170,201,90),(84,91,202,171)], [(1,202,15,216),(2,71,16,57),(3,204,17,218),(4,73,18,59),(5,206,19,220),(6,75,20,61),(7,208,21,222),(8,77,22,63),(9,210,23,224),(10,79,24,65),(11,212,25,198),(12,81,26,67),(13,214,27,200),(14,83,28,69),(29,197,43,211),(30,66,44,80),(31,199,45,213),(32,68,46,82),(33,201,47,215),(34,70,48,84),(35,203,49,217),(36,72,50,58),(37,205,51,219),(38,74,52,60),(39,207,53,221),(40,76,54,62),(41,209,55,223),(42,78,56,64),(85,117,99,131),(86,146,100,160),(87,119,101,133),(88,148,102,162),(89,121,103,135),(90,150,104,164),(91,123,105,137),(92,152,106,166),(93,125,107,139),(94,154,108,168),(95,127,109,113),(96,156,110,142),(97,129,111,115),(98,158,112,144),(114,190,128,176),(116,192,130,178),(118,194,132,180),(120,196,134,182),(122,170,136,184),(124,172,138,186),(126,174,140,188),(141,189,155,175),(143,191,157,177),(145,193,159,179),(147,195,161,181),(149,169,163,183),(151,171,165,185),(153,173,167,187)], [(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28),(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56),(57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84),(85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112),(113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140),(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168),(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196),(197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224)], [(1,14,48,33),(2,32,49,13),(3,12,50,31),(4,30,51,11),(5,10,52,29),(6,56,53,9),(7,8,54,55),(15,28,34,47),(16,46,35,27),(17,26,36,45),(18,44,37,25),(19,24,38,43),(20,42,39,23),(21,22,40,41),(57,68,203,214),(58,213,204,67),(59,66,205,212),(60,211,206,65),(61,64,207,210),(62,209,208,63),(69,84,215,202),(70,201,216,83),(71,82,217,200),(72,199,218,81),(73,80,219,198),(74,197,220,79),(75,78,221,224),(76,223,222,77),(85,190,193,110),(86,109,194,189),(87,188,195,108),(88,107,196,187),(89,186,169,106),(90,105,170,185),(91,184,171,104),(92,103,172,183),(93,182,173,102),(94,101,174,181),(95,180,175,100),(96,99,176,179),(97,178,177,98),(111,192,191,112),(113,118,155,160),(114,159,156,117),(115,116,157,158),(119,140,161,154),(120,153,162,139),(121,138,163,152),(122,151,164,137),(123,136,165,150),(124,149,166,135),(125,134,167,148),(126,147,168,133),(127,132,141,146),(128,145,142,131),(129,130,143,144)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 26 | 10 |
| 0 | 0 | 0 | 28 | 19 | 3 |
| 0 | 0 | 13 | 5 | 1 | 0 |
| 0 | 0 | 24 | 16 | 0 | 1 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 1 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 24 | 27 | 0 |
| 0 | 0 | 5 | 13 | 0 | 27 |
| 0 | 0 | 28 | 0 | 13 | 5 |
| 0 | 0 | 0 | 28 | 24 | 16 |
| 1 | 5 | 0 | 0 | 0 | 0 |
| 17 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 27 | 1 | 1 |
| 0 | 0 | 2 | 24 | 28 | 19 |
| 0 | 0 | 7 | 7 | 27 | 2 |
| 0 | 0 | 22 | 17 | 27 | 5 |
| 28 | 24 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 2 | 28 | 28 |
| 0 | 0 | 24 | 2 | 10 | 1 |
| 0 | 0 | 7 | 7 | 27 | 2 |
| 0 | 0 | 17 | 22 | 24 | 2 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,13,24,0,0,0,28,5,16,0,0,26,19,1,0,0,0,10,3,0,1],[12,1,0,0,0,0,0,17,0,0,0,0,0,0,16,5,28,0,0,0,24,13,0,28,0,0,27,0,13,24,0,0,0,27,5,16],[1,17,0,0,0,0,5,28,0,0,0,0,0,0,2,2,7,22,0,0,27,24,7,17,0,0,1,28,27,27,0,0,1,19,2,5],[28,0,0,0,0,0,24,1,0,0,0,0,0,0,27,24,7,17,0,0,2,2,7,22,0,0,28,10,27,24,0,0,28,1,2,2] >;
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | ··· | 4H | 4I | 4J | 4K | 4L | 4M | ··· | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | - | + | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | 2- (1+4) | Q8⋊2D7 | D4.10D14 |
| kernel | C42.155D14 | C28⋊2Q8 | C42⋊D7 | Dic7⋊3Q8 | C4.Dic14 | D14⋊2Q8 | C4⋊C4⋊D7 | C7×C42.C2 | C42.C2 | C28 | C42 | C4⋊C4 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 4 | 2 | 4 | 1 | 3 | 4 | 3 | 18 | 2 | 6 | 12 |
In GAP, Magma, Sage, TeX
C_4^2._{155}D_{14} % in TeX
G:=Group("C4^2.155D14"); // GroupNames label
G:=SmallGroup(448,1150);
// by ID
G=gap.SmallGroup(448,1150);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,758,219,268,675,297,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=b^2,d^2=a^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=a^2*b^-1,d*b*d^-1=b^-1,d*c*d^-1=a^2*b^2*c^13>;
// generators/relations
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